The invention is based on a fuel injection pump having a pump piston, an adjusting member the position of which determines the duration of the fuel variation effected by the pump piston, and a connecting line leading from the pump work chamber to a fuel withdrawal chamber, the cross section of the connecting line being adjustable by means of a throttle device in order to determine the injection quantity. In a known pump of this kind, the duration of fuel supply is determined by the adjusting member embodied as a governor slide, while the injection quantity is varied by an adjustable bypass throttle parallel to the injection nozzle. The supply duration is thus freely selectable, independently of the injection quantity. The variation of the injection quantity, at a predetermined supply duration, is brought about by the variable cross section of the bypass throttle, which is adjusted in turn, via a hydraulic servomotor and a differential-pressure regulating valve, until such time as the injection quantity per unit of time corresponds to the prespecified value of the differential-pressure valve. The supply duration is arbitrarily varied in accordance with the position of the gas pedal by varying the position of the slide. However, the entire quantity of fuel pumped over the duration of supply does not reach the injection valve. Some of it flows out via the adjustable bypass throttle. In this known fuel injection pump, however, there is no particular provision made for regulating the injection quantity during idling operation.